Rigid Body Impact Research Articles

A novel technique for low-velocity impact of shallow arches

In the current study, an analytical model to analyze the low-velocity impact (LVI) response of metamaterial shallow arches subjected to rigid body impact is presented. The presented nonlinear model considers transverse deformation of the cross-section and geometric nonlinearity based on the higher-order shear theory and von Kármán nonlinearity. The research delves into three key aspects. The first is concerned with the establishment of a contact model to capture the contact characteristics between the impactor and the arch. The second aspect deals with the design of the member with Negative Poisson’s Ratio (NPR). The third aspect is concerned with the asymptotic solution of dynamic equations by using a two-perturbation technique. The proposed model is used to analyze the effects of auxetic, initial deformation, and foundation on the impact response and post-impact vibration of the arch. The results show that the contact area between the sphere impactor and the arch is elliptical. It is also noted that the contact force and indentation are highly dependent on the laminated configuration and auxetic properties. The study reveals that the presented model is a valid technique to evaluate the impact characteristics of metamaterial arches along with optimal design impact resistance of arches.

Simulating Brittle Fracture with Material Points

Large-scale topological changes play a key role in capturing the fine debris of fracturing virtual brittle material. Real-world, tough brittle fractures have dynamic branching behaviour but numerical simulation of this phenomena is notoriously challenging. In order to robustly capture these visual characteristics, we simulate brittle fracture by combining elastodynamic continuum mechanical models with rigid-body methods: A continuum damage mechanics (CDM) problem is solved, following rigid-body impact, to simulate crack propagation by tracking a damage field. We combine the result of this elastostatic continuum model with a novel technique to approximate cracks as a non-manifold mid-surface, which enables accurate and robust modelling of material fragment volumes to compliment fast-and-rigid shatter effects. For enhanced realism, we add fracture detail, incorporating particle damage-time to inform localised perturbation of the crack surface with artistic control. We evaluate our method with numerous examples and comparisons, showing that it produces a breadth of brittle material fracture effects and with low simulation resolution to require much less time compared to fully elastodynamic simulations.

Analysis of Three-Dimensional Rigid-Body Impact with Friction

This paper is concerned with the modeling and simulation of two- and three-dimensional impact in the presence of friction. Single impacts are considered, and the impact equations are solved algebraically. Impact generates impulsive normal and frictional forces and the direction of sliding can change during impact. A procedure is developed to estimate the change in direction of sliding during three-dimensional impact. The modes of impact, such as sliding, sticking, or change in direction of sliding, are classified for both two- and three-dimensional impact. Simulations are conducted to analyze the energy lost, change in impact direction, and stick-slip conditions, where different models for restitution are compared. A closed-form solution is developed to analyze the modes of sliding for two-dimensional impact.

Closed-form solution for shock wave propagation in density-graded cellular material under impact

Density-graded cellular materials have tremendous potential in structural applications where impact resistance is required. Cellular materials subjected to high impact loading result in a compaction type deformation, usually modeled using continuum-based shock theory. The resulting governing differential equation of the shock model is nonlinear, and the density gradient further complicates the problem. Earlier studies have employed numerical methods to obtain the solution. In this study, an analytical closed-form solution is proposed to predict the response of density-graded cellular materials subjected to a rigid body impact. Solutions for the velocity of the impinging rigid body mass, energy absorption capacity of the cellular material, and the incident stress are obtained for a single shock propagation. The results obtained are in excellent agreement with the existing numerical solutions found in the literature. The proposed analytical solution can be potentially used for parametric studies and for effectively designing graded structures to mitigate impact.

Enhanced weakly-compressible MPS method for violent free-surface flows: Role of particle regularization techniques

This paper develops a consistent particle method for capturing the highly non-linear behavior of violent free-surface flows, based on an Enhanced Weakly Compressible Moving Particle Semi-implicit (EWC-MPS) method. It pays special attention to the evaluation and improvement of two particle regularization techniques, namely, pairwise particle collision (PC) and particle shifting (PS). To improve the effectiveness of PC in removing noisy pressure field, and volume conservation issue of PS, we propose and evaluate several enhancements to these techniques, including a novel dynamic PC technique, and a consistent PS algorithm with new boundary treatments and additional terms (in the continuity and momentum equations). Besides, we introduce modified higher-order and anti-symmetric operators for the diffusive and shear force terms. Evaluation of the proposed developments for violent free-surface flow benchmark cases (2D dam-break, 3D water sloshing, and 3D dam-break with an obstacle) confirms an accurate prediction of the flow evolution and rigid body impact, as well as long-term stability of the simulations. The dynamic PC reduces pressure noises with low energy dissipation, and the consistent PS conserves the volume even for extreme deformations. Comparing the role of these new particle regularization techniques demonstrates the effectiveness of both in assuring the uniformity of the particle distribution and pressure fields; nevertheless, the implementation of PS is found to be more complex and time-consuming, mainly due to its need for free surface detection and boundary treatments with several tuning parameters.

Dynamic modeling and simulation of impact in hydraulic cylinders

In this paper, modeling impact dynamics of a piston and its cylinder body in a hydraulic cylinder is investigated. The studied system consists of two identical hydraulic cylinders controlled by a pressure sequence valve. The impact is assumed as a linear one dimensional and purely translational viscoelastic impact of rigid bodies. Four impact models, the Kelvin-Voigt, the Maxwell, the standard-solid, and the Hunt-Crossley, are considered. Measurements of the transient variations of the cylinders operating pressures and both pistons strokes, at different loading conditions, are conducted. A comprehensive dynamic model of the studied system, considering the four models, is deduced. The Kelvin-Voigt model produced tensile forces by the end of the contact period and it resulted in discontinuities in the contact force during its steady state period. Both results are physically impossible in rigid bodies impacting. In the Maxwell model, large amount of discontinuities appeared in the contact force, which causes the piston to make an infinite number of rebounds during the contact period. In the standard-solid model, the discontinuities in the contact force were found to be much less than those of the Maxwell model. As a result, when the impact occurs, the cylinder pressure gets an overshoot accompanied with large oscillations when the Maxwell model is applied, however, these oscillations do not approximately appear when the standard-solid model is applied. The simulation results showed also that the Hunt-Crossley nonlinear model presented very high penetration depth, which is certainly unrealistic in rigid bodies impacting. The validation of the proposed dynamic models showed that the standard-solid is the most suitable model that may represent the impact in the studied cylinders.

Reduced-gravity experiments of nonspherical rigid-body impact on hard surfaces

Ballistic landers enable orbiting asteroid missions to perform surface science at limited additional cost and risk. Due to asteroids’ weak gravity and irregular terrain, lander deployment trajectories will consist of several chaotic bounces. Although impacts on regolith-covered asteroids are numerically expensive to model, impacts on rocky asteroids can be modeled with simpler, impulsive contact models. One such model is that by Stronge, which was successfully used in large-scale Monte Carlo studies of asteroid lander deployment. This model parameterizes impacts with (fixed) material restitution and friction coefficients, but has not been validated for the low-velocity regime of an assembled, nonspherical body. This paper uses an air-bearing setup to perform 2D experiments of a rectangular floating assembly impacting a concrete block with V⩽25 cm/s. The impact velocity, assembly attitude, and block attitude are varied across 2,400 experimental runs of both normal and tangential impacts. Optical tracking is used to extract the pre- and post-impact velocities of the assembly. In a majority of cases, Stronge’s model can be fit to the experiments to extract the corresponding restitution and friction coefficients. We find that the coefficients are not fixed with respect to the impact velocity and attitude, but that their variation is seemingly random. In some tangential impact cases, the model even fails to reproduce the observed behavior althogether. This suggests that there may not be a simple way to reconcile Stronge’s fixed-material-coefficient model with reality, although it may retain practical use if the coefficients are randomly varied in each impact of a simulation.

Landing of hopping rovers on Irregularly-shaped small bodies using attitude control

A hopping rover that is driven only by internal or external attitude actuators is an ideal mobility approach for surface exploration of small solar system bodies. Without thrust control and grasping mechanisms, a hopping rover is mechanically simple to design and less prone to mechanical failures, but faces challenges during soft landing. It may rebound from the surface, causing deviations from its original landing site. In this paper, landing of a hopping rover on the surface of an asteroid is investigated, and a strategy using only attitude control to shorten the landing distance is proposed. Based on rigid body impact dynamics, the edge impact configuration is investigated in detail. The factors that affect the impact states of a cube-shaped hopping rover are studied. Then, controlled edge landing is analyzed, in which the post-impact velocity of the hopping rover is changed by controlling its attitude prior to impact. Three guidance schemes are developed, followed by attitude profile generation and finite time stable attitude control. Finally, simulations are performed on an ideal flat surface and uneven terrain. The results show that controlled edge landing can effectively reduce the landing distance and settling time, compared with uncontrolled landing. This study on hopping motion on the surface of an irregular-shaped asteroid with attitude control, can provide a reference for hopper trajectory plan in future asteroid surface explorations.

Intersection AEB implementation strategies for left turn across path crashes

Objective: Left turn across path with traffic from the opposite direction (LTAP/OD) is the second most frequent car-to-car intersection crash type after straight crossing path (SCP) in Germany and the United States. Intersection automated emergency braking (AEB) for passenger cars can address these crashes.This study investigates 2 implementation strategies of intersection AEB addressing LTAP/OD crashes: (1) only the turning car is equipped with an intersection AEB and (2) turning and straight-heading cars are equipped with an intersection AEB. For each strategy, the influence of a safety zone around the vehicles that should not be entered is evaluated in terms of accident avoidance, injury mitigation, and change in velocity (delta-V) of remaining accidents. Results are given as a function of market penetration.Methods: A total of 372 LTAP/OD crashes from the time series precrash matrix (PCM), a subsample of the German In-Depth Accident Study (GIDAS), were resimulated in the PRediction of Accident Evolution by Diversification of Influence factors in COmputer simulation (PRAEDICO) simulation framework. A Kudlich-Slibar rigid-body impact model and an injury risk curve derived from GIDAS were used to predict remaining moderate to fatal (Maximum Abbreviated Injury Scale [MAIS] 2 + F) injuries among car occupants.Results: With a safety zone of 0.2 m, when the turning vehicle only was equipped with an intersection AEB, 59% of the crashes were avoided at a 100% market penetration. With both vehicles equipped the percentage increased to 77%. MAIS 2 + F injured occupants were reduced by 60 and 76%, respectively. Considering both the turning and the straight-heading vehicles, the delta-V decreased strongly with market penetration in remaining left-side impacts but only slightly in remaining frontal and right-side impacts. Eliminating the safety zone substantially decreases effectiveness in all conditions.Conclusions: Implementation strategy and safety zone definition strongly influence the real-life performance of intersection AEB. AEB should be applied not only for the turning vehicle but also for the straight-going vehicle to benefit from the full potential. Situationally appropriate safety zone definitions, in line with human hazard perception, need more attention and are a key to balance true positive and false positive performance. Remaining delta-V does not decrease broadly; hence, there is no evidence that future LTAP/OD crashes will be generally of lower severity. This highlights the need for continuous development of in-crash protection.

Debris impact under extreme hydrodynamic conditions part 2: Impact force responses for non-rigid debris collisions

Historical tsunami events have resulted in extreme damage to coastal regions worldwide. Among the various loads associated with tsunami waves, debris impact has been shown to cause major damage to nearshore infrastructure. As a result, debris impact loads have been included prominently in existing design guidelines and standards, such as the FEMA P-646 [11] and ASCE7 Chapter 6 [6]. In the present study, single debris impacts on structures was experimentally investigated under tsunami-like wave conditions. Eccentric and oblique impacts of a model shipping container (length scale 1:40) on a non-rigid structure were examined. The experimental results of the non-rigid impacts are discussed in the context of the existing force equations which were derived under the assumption of rigid-body impact theory. As expected, the elasticity of the structure was determined to influence and, specifically, reduce the magnitude of the debris impact forces. Existing impact force equations are herein critically discussed through comparison with the experimental results and, finally, modifications to existing force equations to account for non-rigid collisions are proposed.

Impact characterization of agricultural products by fall trajectory simulation and measurement

Since 40 years, artificial fruits or dummies are built similar to real agricultural produce in order to measure mechanical load caused due to harvest and post-harvest handling systems. As shown by Praeger et al., 2013 the evaluation of how close these electronic fruits reflect real products impact behavior has been largely neglected during their design.The paper dealt with development of a test method for comparison of elastic characteristics of real potato tubers and of dummy materials (built based on 2 component polyurethane elastomers) falling on metal or plastic materials. Therefore, the trajectory of the produce center of the whole drop process was simulated based on measurements with a miniaturised 3-axis accelerometer inside the samples, force measurements at the impact position and videos made with a high speed camera of the fall and rebound process. A simulation model of the impact was developed and impacts were characterised by forces, coefficients of restitutions, accumulated energy and deformation features obtained by quasi- rigid body impact simulations. Exemplary impact characteristics are presented for real potatoes of different water status and artificial tuber dummies using force-deformation courses and coefficients of restitution. The testing procedure showed to be useful for the systematic design of optimised dummy materials, for instance based on polyurethane elastomers, for a highly realistic replication of impact performance of real fruit and to improve the applicability and accuracy of dummies in field measurements. The drop tests and simulations for tuber dummies and real potatoes showed a wide range of impact characteristics when falling onto steel. In general, impact forces of the currently used dummies were higher and deformations were reduced compared to those of potato tubers. One dummy tested in this study showed impact characteristics widely similar to potato tuber material.

Drag torque modeling at high circumferential speed in open wet clutches considering plate wobble and mechanical contact

Abstract A mathematical model is established to predict the drag torque increment due to the mechanical contact at high circumferential speed in open wet clutches. The fluid hydrodynamic actions are coupled simultaneously with the kinematic position of the tilted friction plate. The drag torque due to mechanical contact at high speed is estimated by presenting a rigid-body impact model. The calculation results are validated by experiments performed on an open multi-plate wet clutch test rig. The model calculation demonstrates that the drag torque also becomes higher with larger flow rates of lubricant at high circumferential speed.

МОДЕЛИРОВАНИЕ ПРОНИКАНИЯ НЕОСЕСИММЕТРИЧНЫХ ТЕЛ В ГРУНТ ПО ИНЕРЦИИ ПРИ УЧЕТЕ ТРЕНИЯ

The problem of a normal impact and penetration of rigid spatial bodies of a finite mass into a half-space occupied by an elastoplastic soil medium. The penetrated medium is modeled by linearly compressible elastoplastic Grigoryan medium, with the yield strength linearly depending on pressure. The problem is analyzed in a 3D formulation, using software package LS-DYNA. The elastoplastic penetrated medium is analyzed on a fixed Eulerian grid with empty meshes, where the material flows to in the process of deformation. Spatial strikers are modeled by a rigid non-deformable body in a Lagrangian coordinate system. The effect of surface friction during the penetration of strikers of various forms (a round cone, a four-ray star and a pyramidal body) into elastoplastic Grigoryan soil medium is studied. The cross-section of the star-shaped body is generated by two rhombs with the ration of diagonals of 1:2; the base of the pyramid is a rhomb with the ratio of diagonals of 1:3. The analyzed bodies have equal areas of the bases and equal inclinations of the side surface (the angle between the direction of the motion velocity vector of the body and a normal to the side surface). A circular cone with the same base area is considered for comparison.The considered strikers moved with constant velocities and mechanically, in the velocity range of 150 to 600 m/s, corresponding to subsonic and supersonic velocities. The surface friction coefficient is close to the value of the friction coefficient in sandy soils of natural composition. The results are compared with the earlier obtained computational results for a zero friction coefficient. It is found that resistance to penetration and penetration depth can be described using binomial Resale's penetration law with a quadratic velocity. The disagreement between the forces of resistance to penetration of a pyramidal, conical and star-shaped bodies of the same height are within the interval of 10-20%.

Bounce maps

We present a novel method to enrich standard rigid-body impact models with a spatially varying coefficient of restitution map, or Bounce Map. Even state-of-the art methods in computer graphics assume that for a single rigid body, post- and pre-impact dynamics are related with a single global, constant, namely the coefficient of restitution. We first demonstrate that this assumption is highly inaccurate, even for simple objects. We then present a technique to efficiently and automatically generate a function which maps locations on the object's surface along with impact normals, to a scalar coefficient of restitution value. Furthermore, we propose a method for two-body restitution analysis, and, based on numerical experiments, estimate a practical model for combining one-body Bounce Map values to approximate the two-body coefficient of restitution. We show that our method not only improves accuracy, but also enables visually richer rigid-body simulations.

An impulse-based model for impact between two concrete blocks

Drop-weight tests were conducted on 10 pairs of reinforced concrete cubic blocks with a side length of 250mm to investigate their motion states during the impact process. The collision type was face-to-face collinear impact which was primary collision type in structural collapse due to natural or man-made hazards. Incident velocity and reinforcement ratio were two test variables and the block acceleration histories were measured. A model based on the smooth particle hydrodynamics (SPH) method was developed, verified, and used for parametric studies. Experimental results found that impulses increased almost linearly with the increase in incident velocities of less than 13m/s. However, numerical results indicated that their correlation became nonlinear when incident velocities exceeded 30m/s. The impulses also increased with the increase in mass ratios and decreased almost linearly with the increase in initial impact angles based on numerical studies. These new findings differ from traditional rigid body impact theory. Moreover, parametric studies revealed that the impulses increased linearly with the increase in block masses and concrete compressive strengths. Reinforcement ratios had no effect on the impulse and acceleration history of colliding blocks based on experimental and numerical studies. Finally, an impulse-based model was introduced to predict motion state after impact and had good correlation with the experimental data.

Numerical Study of the Orientation of Cylindrical Particles in a Circulating Fluidized Bed

Orientation is pivotal in circulating fluidized beds using cylinder-shaped particles. This study developed a three-dimensional multiway coupling model for predicting the orientation of cylindrical particles in circulating fluidized beds. The coupling algorithm between motorial cylindrical particles and the turbulence was established by incorporating the correlation between Lagrangian time scales and the k–e model. Collisions among cylindrical particles were solved by combining rigid body impact dynamics with the hard sphere model. The results showed that the majority of cylindrical particles are prone to align with the streamline, which is in good agreement with the experimental observation. Cylindrical particles become more oriented along rising height position in the riser, increasing the slenderness ratio and decreasing the distance to the wall. Under turbulence conditions, the effect of Reynolds number on the orientation of cylindrical particles was found to be marginal.

Direct Measure of Rigid Body Accelerations for Wave Impact of a Planing Hull

Measurements of accelerations during wave impact of a planing hull are usually contaminated by nonhydrodynamic disturbances inherent in full-scale tests and by vibrations induced by the test model and towing carriage in towing tank tests. As a consequence, researchers have resorted to the use of electronic filters to extract rigid body hydrodynamic impact accelerations. This article first calculates the rigid body impact acceleration time histories of 2dimensional deadrise wedges impacting on a level water surface as a function of initial contact velocity, deadrise angle, and unit drop weight. It also calculates the spectral content of these time histories. It then demonstrates how the time histories, time to peak, and spectral content of these 2D wedges are distorted by the use of standard "one-way" electronic filters when processing the data. In a sense, this section of the article can be taken as a simple tutorial on the impact process. The Davidson Laboratory suggests and demonstrates the use of a rigid "free-running" model that is not rigidly connected to the towing carriage and is thus devoid of carriage-induced disturbances. This obviates the use of filters in processing the recorded data. Hence, the directly measured impact accelerations are thus rigid body hydrodynamic accelerations. These are compared with measurements made with the model rigidly attached to the carriage to demonstrate its effect on contaminating the recorded hydrodynamic signal. It is recommended that other towing tanks consider the use of this or other "free-model" test procedures to identify the possible contamination of the recorded acceleration time histories introduced by their carriage and model disturbances. It is also recommended that for those full-scale tests, where the "Standard G" method of data reduction has been applied, that a model be built and tested using the "free-model" test procedure suggested in this article. This will compare the derived rigid body accelerations with the true hydrodynamic impact accelerations as obtained in these free-model tests.

Direct Measure of Rigid Body Accelerations for Wave Impact of a Planing Hull

Measurements of accelerations during wave impact of a planing hull are usually contaminated by nonhydrodynamic disturbances inherent in full-scale tests and by vibrations induced by the test model and towing carriage in towing tank tests. As a consequence, researchers have resorted to the use of electronic filters to extract rigid body hydrodynamic impact accelerations. This article first calculates the rigid body impact acceleration time histories of two-dimensional deadrise wedges impacting on a level water surface as a function of initial contact velocity, deadrise angle, and unit drop weight. It also calculates the spectral content of these time histories. It then demonstrates how the time histories, time to peak, and spectral content of these 2D wedges are distorted by the use of standard “one-way” electronic filters when processing the data. In a sense, this section of the article can be taken as a simple tutorial on the impact process. The Davidson Laboratory suggests and demonstrates the use of a rigid “free-running” model that is not rigidly connected to the towing carriage and is thus devoid of carriage-induced disturbances. This obviates the use of filters in processing the recorded data. Hence, the directly measured impact accelerations are thus rigid body hydrodynamic accelerations. These are compared with measurements made with the model rigidly attached to the carriage to demonstrate its effect on contaminating the recorded hydrodynamic signal. It is recommended that other towing tanks consider the use of this or other “free-model” test procedures to identify the possible contamination of the recorded acceleration time histories introduced by their carriage and model disturbances. It is also recommended that for those full-scale tests, where the “Standard G” method of data reduction has been applied, that a model be built and tested using the “free-model” test procedure suggested in this article. This will compare the derived rigid body accelerations with the true hydrodynamic impact accelerations as obtained in these free-model tests.

Impact fracture analysis enhanced by contact of peridynamic and finite element formulations

A new contact algorithm is implemented for the interaction of peridynamic regime and finite elements for the effective impact fracture analysis. The region that might experience fracture is modeled using peridynamics that is a reformulated theory of continuum mechanics while the impact projectile is modeled by three-dimensional finite elements in order to exploit mutual advantages of the formulations. An inverse isoparametric mapping technique and a node-to-surface contact algorithm are customized and implemented, and a penalty method enforcing displacement constraints is then incorporated for the transient analyses using the explicit time integration. The proposed numerical technique is applied to several examples for verification and validation. Starting with examining the material behavior of a peridynamic bar, rigid-body impact is then studied for the verification of contact-impact procedure. The ballistic perforation of an impactor through a steel plate is investigated numerically. Good agreement between numerical simulations and the analytical model is observed in the analysis of the residual velocities. The physical process of perforation is captured accurately in the simulations using the proposed numerical methodology.

An experimental study on the local failure prevention of plate/wall members subjected to rigid body impact

An experimental study on the local failure prevention of plate/wall members subjected to rigid body impact